메뉴 건너뛰기




Volumn 318, Issue 1, 2000, Pages 181-204

Rough isometry and energy finite solutions of elliptic equations on Riemannian manifolds

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0034373507     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002080000118     Document Type: Article
Times cited : (6)

References (27)
  • 1
    • 84968508874 scopus 로고
    • On complete manifolds with nonnegative Ricci curvature
    • U. Abresch and D. Gromoll: On complete manifolds with nonnegative Ricci curvature, J. Amer. Math. Soc. 6 (1990), 355-374
    • (1990) J. Amer. Math. Soc. , vol.6 , pp. 355-374
    • Abresch, U.1    Gromoll, D.2
  • 2
    • 0000720752 scopus 로고
    • A note on the isoperimetric constant
    • P. Buser: A note on the isoperimetric constant, Ann. Sci. Ec. Norm. Sup. Paris 15 (1982), 213-230
    • (1982) Ann. Sci. Ec. Norm. Sup. Paris , vol.15 , pp. 213-230
    • Buser, P.1
  • 3
    • 84972500359 scopus 로고
    • The splitting theorem for manifolds of nonnegative Ricci curvature
    • J. Cheeger and D. Gromoll: The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geom. 6 (1971), 119-128
    • (1971) J. Differential Geom. , vol.6 , pp. 119-128
    • Cheeger, J.1    Gromoll, D.2
  • 4
    • 0042633317 scopus 로고
    • Variétés riemanniennes isométriques à l'infini
    • Th. Coulhon and L. Saloff-Coste: Variétés riemanniennes isométriques à l'infini, Rev. Mat. Iberoamericana 11 (1995), 687-726
    • (1995) Rev. Mat. Iberoamericana , vol.11 , pp. 687-726
    • Coulhon, Th.1    Saloff-Coste, L.2
  • 5
    • 0039285109 scopus 로고
    • Bounded harmonic functions and positive Ricci curvature
    • H. Donnelly: Bounded harmonic functions and positive Ricci curvature, Math. Z. 191 (1986), 559-565
    • (1986) Math. Z. , vol.191 , pp. 559-565
    • Donnelly, H.1
  • 6
    • 0040861386 scopus 로고
    • Set of positive solutions of Laplace-Beltrami equation on special type of Riemannian manifolds
    • A. A. Grigor'yan: Set of positive solutions of Laplace-Beltrami equation on special type of Riemannian manifolds, Izv. Vyssh. Uchebn. Zaved., Matematika (1987) no.2, 30-37: English transi. Soviet Math. (Iz, VUZ) 31 (1987), no.2, 48-60
    • (1987) Izv. Vyssh. Uchebn. Zaved., Matematika , Issue.2 , pp. 30-37
    • Grigor'yan, A.A.1
  • 7
    • 0040861200 scopus 로고
    • English transl.
    • A. A. Grigor'yan: Set of positive solutions of Laplace-Beltrami equation on special type of Riemannian manifolds, Izv. Vyssh. Uchebn. Zaved., Matematika (1987) no.2, 30-37: English transi. Soviet Math. (Iz, VUZ) 31 (1987), no.2, 48-60
    • (1987) Soviet Math. (Iz, VUZ) , vol.31 , Issue.2 , pp. 48-60
  • 8
    • 0000844770 scopus 로고
    • On Liouville theorems for harmonic functions with finite Dirichlet integral
    • A. A. Grigor'yan: On Liouville theorems for harmonic functions with finite Dirichlet integral, (In Russian) Matem. Sbornik 132 (1987), no.4, 496-516: English transl. Math. USSR Sbornik 60 (1988), no.2, 485-504
    • (1987) (In Russian) Matem. Sbornik , vol.132 , Issue.4 , pp. 496-516
    • Grigor'yan, A.A.1
  • 9
    • 0000589878 scopus 로고
    • English transl.
    • A. A. Grigor'yan: On Liouville theorems for harmonic functions with finite Dirichlet integral, (In Russian) Matem. Sbornik 132 (1987), no.4, 496-516: English transl. Math. USSR Sbornik 60 (1988), no.2, 485-504
    • (1988) Math. USSR Sbornik , vol.60 , Issue.2 , pp. 485-504
  • 10
    • 0002688660 scopus 로고
    • Dimension of space of harmonic functions
    • A. A. Grigor'yan: Dimension of space of harmonic functions, Mat. Zametki 48(5), (1990) 55-61: English transl. in Math. Notes. 48 (1990), 1114-1118
    • (1990) Mat. Zametki , vol.48 , Issue.5 , pp. 55-61
    • Grigor'yan, A.A.1
  • 11
    • 0007378650 scopus 로고
    • English transl.
    • A. A. Grigor'yan: Dimension of space of harmonic functions, Mat. Zametki 48(5), (1990) 55-61: English transl. in Math. Notes. 48 (1990), 1114-1118
    • (1990) Math. Notes. , vol.48 , pp. 1114-1118
  • 14
    • 0001090134 scopus 로고
    • Rough isometrics and p-harmonic functions with finite Dirichlet integral
    • I. Holopainen: Rough isometrics and p-harmonic functions with finite Dirichlet integral, Rev. Mat. Iberoamericana 10 (1994), 143-176
    • (1994) Rev. Mat. Iberoamericana , vol.10 , pp. 143-176
    • Holopainen, I.1
  • 15
    • 51249165301 scopus 로고
    • Solutions of elliptic equations on manifolds with roughly Euclidean ends
    • I. Holopainen: Solutions of elliptic equations on manifolds with roughly Euclidean ends, Math. Z. 217 (1994), 459-477
    • (1994) Math. Z. , vol.217 , pp. 459-477
    • Holopainen, I.1
  • 16
    • 0039530432 scopus 로고    scopus 로고
    • Volume growth, Green's functions and parabolicity of ends
    • I. Holopainen: Volume growth, Green's functions and parabolicity of ends, Duke Math. J. 97 (1999), no.2, 319-346
    • (1999) Duke Math. J. , vol.97 , Issue.2 , pp. 319-346
    • Holopainen, I.1
  • 17
    • 84972557750 scopus 로고
    • Rough isometries, and combinatorial approximations of geometries of non-compact Riemannian manifolds
    • M. Kanai: Rough isometries, and combinatorial approximations of geometries of non-compact riemannian manifolds, J. Math. Soc. Japan 37 (1985), no.3, 391-413
    • (1985) J. Math. Soc. Japan , vol.37 , Issue.3 , pp. 391-413
    • Kanai, M.1
  • 18
    • 84972571397 scopus 로고
    • Rough isometries and the parabolicity of Riemannian manifolds
    • M. Kanai: Rough isometries and the parabolicity of riemannian manifolds, J. Math. Soc. Japan 38 (1986), no.2, 227-238
    • (1986) J. Math. Soc. Japan , vol.38 , Issue.2 , pp. 227-238
    • Kanai, M.1
  • 21
    • 0033161734 scopus 로고    scopus 로고
    • Rough isometry and Dirichlet finite harmonic functions on Riemannian manifolds
    • Y. H. Lee: Rough isometry and Dirichlet finite harmonic functions on Riemannian manifolds, manuscripta math. 99 (1999), 311-328
    • (1999) Manuscripta Math. , vol.99 , pp. 311-328
    • Lee, Y.H.1
  • 22
    • 0000444319 scopus 로고
    • Positive harmonic functions on complete Riemannian manifolds with non-negative curvature outside a compact set
    • P. Li and L-F. Tam: Positive harmonic functions on complete Riemannian manifolds with non-negative curvature outside a compact set, Ann. of Math. (2) 125 (1987), 171-207
    • (1987) Ann. of Math. (2) , vol.125 , pp. 171-207
    • Li, P.1    Tam, L.-F.2
  • 23
    • 84972525278 scopus 로고
    • Green's functions, harmonic functions, and volume comparison
    • P. Li and L-F. Tam: Green's functions, harmonic functions, and volume comparison, J. Differential Geom. 41 (1995), 277-318
    • (1995) J. Differential Geom. , vol.41 , pp. 277-318
    • Li, P.1    Tam, L.-F.2
  • 24
    • 0002346286 scopus 로고
    • Ball covering property and nonnegative Ricci curvature outside a compact set
    • Z-D. Liu: Ball Covering Property and Nonnegative Ricci curvature Outside a Compact Set, Proc. Symp. Pure Math. 54 (1993), 459-464
    • (1993) Proc. Symp. Pure Math. , vol.54 , pp. 459-464
    • Liu, Z.-D.1
  • 27
    • 84980178548 scopus 로고
    • Harmonic functions on complete Riemannian manifolds
    • S. T. Yau: Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201-228
    • (1975) Comm. Pure Appl. Math. , vol.28 , pp. 201-228
    • Yau, S.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.